To be clear, are you using the Outlook app, or Outlook on the web via a browser like Firefox or Safari?
I use Outlook on the web (don't like the app) and when I cleared my cache and cookies the problem was solved.
They reorganized the layout for no good reason, making it harder to figure out where to change various settings.
So, on the web, you go to the top left menu options and click on "View". Then right underneath are a list of menu options: you click on "Layout", and the option to show or hide the folder pane is there.
After I cleared the cache the folder pane stayed open after I closed an reopened the browser.
Anyway, hope that helps. If you're using the app, good luck.